Oil prices sank more than 2 percent on Tuesday, posting a nine-month closing low, on signs of rising production in key parts of the world.

West Texas Intermediate crude oil futures ended Tuesday's session at $43.23, down 97 cents, the weakest settlement since Sept. 16. The U.S. benchmark fell as low as $42.75, the lowest intraday price since Nov. 14, when the contract hit $42.20 a barrel.

WTI fell more than 20 percent from its 52-week closing and intraday highs, putting the commodity in bear market territory.

Prices for WTI's August contract, which became the front-month after the settle, fell 92 cents to $43.51. Trading volume was concentrated in the August contract on Tuesday.

U.S. WTI contract for August

International benchmark Brent crude prices also fell to a seven-month intraday low.

Output from the 14-member exporter group ticked higher in May due to rising production in Nigeria, Libya and Iraq, raising concerns about OPEC's effort to shrink global stockpiles of crude oil. OPEC and other producers have committed to keeping 1.8 million barrels a day off the market through March.

Libya's oil production rose more than 50,000 barrels per day to 885,000 bpd, a Libyan source told Reuters. Meanwhile, exports of Nigeria's benchmark Bonny Light crude oil are set to rise by 62,000 barrels per day in August, Reuters reported.

Oil prices are "most definitely" heading to $40 a barrel and will likely dip into the upper $30s, John Kilduff, founding partner at energy hedge fund Again Capital, told CNBC's "Squawk Box" on Tuesday.

The market is turning lower in part on tanker-tracking data showing unsold crude oil cargoes from Nigeria, he said. U.S. production is also a concern because American drillers locked in prices for future delivery, and so they'll keep pumping even as near-term prices fall, according to Kilduff.

"Not only do we have a struggle with production and an ineffectual OPEC, non-OPEC production regime, but you have this overhang again that is not clearing, and so that is what this market is reacting to," he said.

"Now we're in the process of the market playing chicken with OPEC and non-OPEC," Kilduff added. The producers are "going to have to react again in a significant way to get the price to stabilize and go back up."

The market has been waiting for signs that OPEC's strategy is achieving its stated goal: driving global crude stockpiles down to the five-year average. Last week, the International Energy Agency warned inventories might not fall to that level until close to the expiration of OPEC's current deal in March.

In this environment, Brent is unlikely to rise much above $50 a barrel, said Ole Hansen, head of commodity strategy at Saxo Bank.

"The market really is in desperate need of data, and the question is if data can improve fast enough over the coming couple months for that to happen," he told CNBC on Tuesday.

However, surging U.S. production may be starting to respond to falling oil prices, Hansen said. Weekly increases in the nation's output have been increasing at a slower pace in the last couple of months than in the prior two months, he noted.

While American drillers did indeed lock in higher prices earlier this year, the drop in oil futures has caught them by surprise, Hansen added. As some of their price hedges expire, the oil market may start to stabilize in the third quarter, he said.